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U.P.B. Sci. Bull., Series C, Vol. 81, Iss. 3, 2019 ISSN 2286-3540
ADVANCED CONTROL SYSTEM FOR PHOTOVOLTAIC
POWER GENERATION, STORAGE AND CONSUMPTION
Cristian MIRON1, Severus OLTEANU2, Nicolai CHRISTOV3, Dumitru
POPESCU4
This paper deals with the implementation of a system architecture for a
photovoltaic (PV) module, assuring regulated voltage output at the consumer,
maximum power point tracking (MPPT) as well as controlled storage of surplus
energy. The usefulness of developing a simple to implement approach that can be
applied to low power PV panels stems from the need to optimize shading effects that
are common in PV arrays installed inside habitable areas. A first dc/dc buck
converter attached to the PV module is controlled through a P&O approach, and a
second buck converter is controlled through a polynomial model-based regulator.
An electronic implementation on a small PV panel accompanied by a 12 V
accumulator validates the results.
Keywords: renewable energy, photovoltaic system, system modeling, polynomial
control.
1. Introduction
The advance in research concerning MPPT algorithms is obvious through
the many electronic solutions and control methods developed as [4]. Usually buck
and boost converters are used, but other solutions are also adopted as the SEPIC
[6]. In this work, a consecutive buck configuration is chosen because of its
simplicity.
The Buck-Boost structures has been thoroughly analyzed and diverse
control solutions have been given as [3]. The article deals with a less used
structure that fits well for some cases of high voltage photovoltaic panels
connected to lower voltage consumers. The proposed architecture works well for
such particular cases, as the generated voltage being high enough will permit the
buck converter that deals with the MPPT to reduce the output voltage in an
acceptable range.
1 University Lille 1 Science and Technology of Lille, France, e-mail: [email protected] 2 As. Prof., Faculty of Automatic Control and Computers, University POLITEHNICA of
Bucharest, Romania, e-mail: [email protected] 3 Prof., University Lille 1 Science and Technology of Lille, France, e-mail: nicolai.christov@univ-
lille.fr 4 Prof., Faculty of Automatic Control and Computers, University POLITEHNICA of Bucharest,
Romania
4 Cristian Miron, Severus Olteanu, Nicolai Christov, Dumitru Popescu
The interest in the control of individual photovoltaic panels stems not only
from the usage of isolated consumers as for example LED based lighting
solutions, but also from the perspective of optimizing a large array of panels
situated in habitable areas where partial shading cannot be avoided. This is of high
interest in current time.
For the MPPT solution itself, a P&O approach is implemented, based on
[2]. These solutions are simple to implement numerically and do not require
knowledge of the system model. Although they have been well researched and
tested in the literature [1],[11],[12], we have chosen such a solution instead of a
more complex one like a sliding mode MPPT as in [5] or Takagi-Sugeno one as in
[7],[10], because we wanted an as simple to implement algorithm that responds to
the industrial demands.
Thus, the paper’s contribution comes from the numerical simplicity of the
architecture, where the second buck converter is a basic, yet powerful model
based polynomial controller; this is important as the two converters influence one
another, and a more robust control is in order.
The paper begins by presenting the architecture as a whole, followed by a
detailed description of the converters, the MPPT approach and the RST regulator.
Finally, results are shown both in simulation and on the hardware test platform,
and conclusions are presented.
2. System Architecture
In Fig. 1. The overall system architecture is presented. In the validated
scenario, the main load connected to the buck converter is a resistive load (as a
heating element or light bulbs). Between the two converters, an auxiliary
resistance can be added as well if required (for example for cooling the unit or for
local lighting of the system).
Fig. 1. The overall system architecture
Considering the transistor in the second buck converter, its switching affects the
first converter as well, as a continuous variation of the equivalent impedance.
Advanced control system for photovoltaic power generation, storage and consumption 5
As such, the current oscillates, but its mean value remains constant for a constant
input voltage. The buck converters work with an 32Khz frequency command. The
inductance value is chosen accordingly, with a value of 160 [µH]. The
condensers, at the output we have 220 [µF], and at the input 100 [µF] to smoothen
the input.
3. Model based polynomial control
In order to control the output voltage, the dynamical model of the second buck
converter has to be developed. The associated transfer function of the process is:
(1)
where , and .
The mathematical model of the discretized process is an auto-regressive
model with exogenous input (ARX). After using the “zero order hold”
discretization method [9] the following discrete transfer function of the model is
obtained for a sampling time of 62.5 µs:
(2)
A polynomial R-S-T algorithm ([8]) is proposed for controlling the plant
model above. The demanded performances are adjusted through some trials
simulating the behavior of the global system, including the photovoltaic generator,
the converters, variable solar irradiation and temperature.
Fig. 2. RST feedback diagram
This control structure takes into account the discretized transfer function
of the process, the R-S-T polynomials used for controlling the plant in closed loop
and rejecting the disturbances, and the trajectory generator which imposes a
desired trajectory. The general RST command form is the following:
6 Cristian Miron, Severus Olteanu, Nicolai Christov, Dumitru Popescu
(3)
Where the polynomials of the controller are defined as below:
(4)
The polynomials of the plant are defined as below:
(5)
The coefficients of the plant can be substituted with the values obtained in
eq. 2. Further we can compute the transfer function of the closed loop system:
(6)
where the poles of the closed loop system are characterized by the polynomial:
(7)
The polynomial P contains the dominant and auxiliary poles of the closed
loop system:
(8)
corresponds to the dominant closed loop poles of the system and
is responsible with for performances of the controller. stands for the
auxiliary poles of the closed loop system, which are used for filtering purposes,
for the improving the robustness of the system. As mentioned in [9], the auxiliary
poles are faster than the dominant poles, meaning that the real part of the roots of
is inferior to one of . A second-degree transfer function is used
for imposing the dominant poles, thus the desired behavior of the closed loop
system; having as the damping factor and the natural frequency. Considering
the value of the sampling period (62.5 μs), a damping factor and a natural
frequency rad/s are chosen. After the discretization we obtain:
(9)
Then we impose these poles to the polynomial P:
(10)
Furthermore, an integrator is added in the Hs imposed part of the
polynomial S in order to obtain a null steady state error. (11)
Advanced control system for photovoltaic power generation, storage and consumption 7
The coefficients of the R and S polynomials are determined by solving the
next equation:
(12)
where:
(13)
and is the Sylvester matrix, associated to the coprime
polynomials A and B. The values are computed:
(14)
(15)
The coefficients of the T polynomial are determined from the following
expression:
(16)
where:
(17)
After introducing eq. (18) in (17) we obtain:
(18)
The transfer function of the tracking reference model is:
(19)
To obtain the polynomials Am and Bm of the trajectory generator, another
transfer function of second degree is used. A damping factor and a natural
frequency rad/s are chosen. The same procedure is applied as for
computing the polynomials R and S.
(20)
(21)
After obtaining all the parameters of the above-mentioned polynomials the
performances of the control algorithm are tested in simulation, as shown in Fig. 3.
The control loop is tested on the model of the DC/DC buck converter in
Matlab-Simulink. During the simulation, two types of disturbances are being
8 Cristian Miron, Severus Olteanu, Nicolai Christov, Dumitru Popescu
applied to the control loop. After the reference is reached, the element of
execution, the transistor from the Sziklai pair, is being disconnected from the
controller. Later on, an additive disturbance is applied to the control law. We can
observe that in Fig. 3 that the MPPT control algorithm is harvesting the maximum
power that the PV can provide, with respect to the second control loop which
perturbs it as well.
Furthermore, we can observe the two types of disturbances proposed
earlier. The first one which is triggered during the time interval [0.4s, 0.41s] is not
well rejected, because the control law is saturated at maximum value, while the
static error is superior to 13.3%. The second one which is triggered during the
time interval [0.8s, 0.85s] is well rejected.
Fig. 3. Closed loop control with the R-S-T control polynomial
4. Robust RST control algorithm
An output sensitivity functions is used to analyze the performances of the
controller:
(22)
We shall consider the margin modulus:
(23)
Advanced control system for photovoltaic power generation, storage and consumption 9
(24)
A bigger value of implies a better robustness. In order to achieve it, the value
of Syp must decrease.
Fig. 4. Sensitivity function – Syp (R-S-T)
In the Fig. 4. is presented the sensitivity function Syp. After computing
with the WinReg Robustness Analysis routine we obtain . The
performances in regulation and tracking can be improved tracking by introducing
auxiliary pairs of poles/zeros and/or introducing pre-specifications for the R and S
polynomials.
Next, we shall create a robust R-S-T polynomial controller. An extra pair
of complex poles to the tracking, imposing another second-degree transfer
function with a damping factor and a natural frequency rad/s.
Poles and zeros of the system can be pre-specified in the polynomial and as
presented below: (25)
The following poles will be imposed:
(26)
The values of all the polynomial are recomputed:
(27)
(28)
10 Cristian Miron, Severus Olteanu, Nicolai Christov, Dumitru Popescu
(29)
(30)
(31)
As for the first RST computed controller, the closed loop control is tested
in WinReg software for reference tracking and rejection of the disturbance for
both robust and standard controllers. A slight improvement related to the rejection
of the disturbances, with the tradeoff of having a higher amplitude of the control
signal. Next, we shall analyze the sensitivity functions of the two controllers, as
presented in Fig. 5.
Fig. 5. Sensitivity functions – Syp (R-S-T) of robust controller vs standard controller
An improved value of is obtained. Then, the control loop
is tested on the model of the DC/DC buck converter, as presented in the figure
below. We can observe in Fig. 6 that the rejection of both types of disturbances is
slightly improved.
Advanced control system for photovoltaic power generation, storage and consumption 11
Fig. 6. Rejection of disturbances (scenario II) – robust vs. standard RST
5. Robust RST control system with anti-windup
During the first type of perturbation we can observe that the command is
saturated. Therefore, an anti-windup technique can be used to avoid this kind of
scenarios.
Fig. 7. RST feedback diagram with anti-windup
The error between the control law generated by the controller and its value
after the saturation block can be multiplied with a gain and be reintroduced in the
control loop, as presented in Fig. 7. The new controller is tested within the same
conditions. The results presented in Fig. 8 confirm us that the new control law is
12 Cristian Miron, Severus Olteanu, Nicolai Christov, Dumitru Popescu
improved. The command is not saturated anymore in the first testing scenario,
aspect which leads to a fast rejection of the disturbance.
Fig. 8. Closed loop control with the robust R-S-T control polynomial with anti-windup
In Fig. 9 is described the implementation of the DC/DC step down
converter.
Fig. 9. Hardware implementation DC/DC
Advanced control system for photovoltaic power generation, storage and consumption 13
The Arduino Uno measures the voltage of the panel delivered via a voltage
divider circuit, and the current of the panel provided by a Hall effect current
sensor. It controls the DC/DC converter via a 32Kh frequency output pin which is
connected to a Sziklai pair or complementary Darlington. For the achieving the
imposed performances a loop that runs at a frequency of 16kHz was used. First
the code was run on an Arduino Uno architecture. The frequency of the control
loop was limited to maximum 3kHz.
The performances of the regulator were not satisfactory if the output was
measured with an oscilloscope. Therefore, a change of architecture was required,
which lead to the use of Arduino Due. The obtained results are presented in Fig.
10. The reference of 12V for charging the battery is well tracked by the controller.
Fig. 10. Implementation of RST controller on Arduino Due
There are some spikes in measurement data, because of the really high
resolution that was used to measure with the oscilloscope.
6. Conclusions
This paper dealt with the design of an architecture for the optimal usage of
photovoltaic energy.
The approach is based on a Buck converter configuration, where the first
converter is controlled through an improved P&O approach, whereas the second
converter is controlled through a polynomial RST algorithm that needed to be
robust enough to reject perturbations risen from the influence of the MPPT
converter. The solution is well suited for high voltage PV panel arrays, offering an
un-expensive solution that can be easily reproduced for all PV modules.
14 Cristian Miron, Severus Olteanu, Nicolai Christov, Dumitru Popescu
The solution was validated in an electrical simulation on a small
photovoltaic panel giving good results. As a perspective, this approach is to be
improved with better control algorithms for the MPPT part, as the P&O is not the
best solution.
The sampling period has been chosen in an optimal way in order to be
large enough to be simple in its numerical implementation yet small enough to
give good results. The sampling period, for reading the sensors and converting the
values to numerical format, needs to be fast enough, considering the 30Khz PWM
frequency.
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